Salt-induced effective interactions and phase separation of an ultrasoft model of polyelectrolytes

We use a semi-grand canonical version of mean-field density functional theory to determine the total effective interaction energy of a solution of penetrable polyions characterised by a Gaussian charge distribution, in the presence of added salt. We then apply this effective representation of semi-flexible polyelectrolyte chains to investigate the possibility of a phase separation similar to that predicted earlier for charge-stabilised hard-sphere colloids. Apart from the absence of a hard-core repulsion, the effective pair potential is similar to the familiar Derjaguin-Landau-Verwey-Overbeek (DLVO) potential between charged-stabilised colloids, i.e. of the screened-Coulomb (Yukawa) form, but the effective valence of the polyions differs significantly from that of the DLVO pair potential, especially at high salt concentration. The existence of a well-defined closed-loop spinodal curve predicted by our mean-field calculation points to a phase separation between solutions with high and low polyion concentrations under reasonable physical conditions. The salt concentration at the upper critical point is typically two orders of magnitude larger than in the case of hard-core polyions, indicating that polyion penetrability appears to enhance the tendency towards phase separation.     

Effects of counterion fluctuations in a polyelectrolyte brush

We investigate the effect of counterion fluctuations in a single polyelectrolyte brush in the absence of added salt by systematically expanding the counterion free energy about Poisson-Boltzmann mean-field theory. We find that for strongly charged brushes, there is a collapse regime in which the brush height decreases with increasing charge on the polyelectrolyte chains. The transition to this collapsed regime is similar to the liquid-gas transition, which has a first-order line terminating at a critical point. We find that, for monovalent counterions, the transition is discontinuous in theta solvent, while for multivalent counterions, the transition is generally continuous. For collapsed brushes, the brush height is not independent of grafting density as it is for osmotic brushes, but scales linear with it.Received: 26 November 2003, Published online: 11 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Scaling Theory of Polyelectrolyte Nanogels

The present paper develops the scaling theory of polyelectrolyte nanogels in dilute and semidilute solutions.The dependencies of the nanogel dimension on branching topology, charge fraction, subchain length, segment number,solution concentration are obtained. For a single polyelectrolyte nanogel in salt free solution, the nanogel may be swelled by the Coulombic repulsion(the so-called polyelectrolyte regime) or the osmotic counterion pressure(the so-called osmotic regime). Characteristics and boundaries between different regimes of a single polyelectrolyte nanogel are summarized.In dilute solution, the nanogels in polyelectrolyte regime will distribute orderly with the increase of concentration. While the nanogels in osmotic regime will always distribute randomly. Different concentration dependencies of the size of a nanogel in polyelectrolyte regime and in osmotic regime are also explored.     

Optimal cell approach to osmotic properties of finite stiff-chain polyelectrolytes

We propose a self-consistent geometry optimized cell model approach to study osmotic properties of stiff-chain polyelectrolyte solutions. In contrast with the usual monotonic Poisson-Boltzmann prediction, the cell model predicts the correct nonmonotonic dependence of the osmotic coefficient on concentration. A lower degree of polymerization is found to reduce significantly the counterion condensation in a typical dilute strong polyelectrolyte. The results agree quantitatively with simulations of a corresponding many-body bulk system up to a dense semidilute regime.     

Scaling equations for a biopolymer in salt solution

The effect of the simultaneous presence of monovalent and divalent cations on the thermodynamics of polyelectrolyte solutions is an incompletely solved problem. In physiological conditions, combinations of these ions affect structure formation in biopolymer systems. Dynamic light scattering measurements of the collective diffusion coefficient D and the osmotic compressibility of semidilute hyaluronan solutions containing different ratios of sodium and calcium ions are compared with simple polyelectrolyte models. Scaling relationships are proposed in terms of polymer concentration and ionic strength J of the added salt. Differences in the effects of sodium and calcium ions are found to be expressed only through J.     

Ion-Exchange selectivity coefficients in the exchange of calcium,strontium, cobalt,nickel, zinc,and cadmium ions with hydrogen ion in variously cross-linked polystyrene sulfonate cation exchangers at 25°C

The ion-exchange selectivity parameters for the exchange of trace calcium, strontium, cobalt, nickel, zinc, and cadmium ions with hydrogen ion in cross-linked polystyrene-sulfonic acid cation exchangers have been determined from equilibrium ionic distribution measurements at 25°C in dilute solutions of perchloric acid and polystyrene-sulfonic acid. The selectivity behavior in perchloric acid solutions shows that the divalent ion is always preferred by the resin phase. The selectivity coefficients are a smooth function of resin phase concentration, increasing with concentration for Sr²⁺ more than for Ca²⁺ and Cd²⁺ and being practically independent of resin phase concentration for Co²⁺, Ni²⁺, and Zn²⁺. The selectivity coefficients measured in salt-free solutions of polystyrene-sulfonic acid show a marked dependence on the polyelectrolyte concentration, the divalent ion being preferred by the aqueous phase. This preference diminishes with the concentration of polyelectrolyte. These results are interpreted by resort to the Gibbs-Duhem equation. This thermodynamic analysis has been facilitated by the availability of osmotic coefficient data for the pure polyelectrolyte ion forms over a large concentration range. Ion-exchange selectivity predictions by using this approach accurately reflect the observed ion-exchange selectivity behavior.     

Formation and stability of coreless vortex dipoles in phase-separated binary condensates

We study the motion of the Gaussian obstacle potential created by a blue detuned laser beam through a phase-separated binary condensate in the pancake-shaped traps. We show that phase-separated binary condensates like ⁸⁵Rb–⁸⁷Rb, with appropriate interaction parameters, can be used experimentally to create obstacle assisted droplet and coreless vortex dipoles. We theoretically analyze the energetic stability of condensates with normal and coreless vortices. We confirm our analytic and semi-analytic results by numerical solutions of coupled Gross–Pitaevskii equations.     

Non-linear osmotic brush regime: Simulations and mean-field theory

We investigate polyelectrolyte brushes in the osmotic regime using both theoretical analysis and molecular dynamics simulation techniques. In the simulations at moderate Bjerrum length, we observe that the brush height varies weakly with grafting density, in contrast to the accepted scaling law, which predicts a brush thickness independent of the grafting density. We show that such behavior can be explained by considering lateral electrostatic effects (within the non-linear Poisson-Boltzmann theory) combined with the coupling between lateral and longitudinal degrees of freedom due to the conserved polymer volume (which are neglected in scaling arguments). We also take the non-linear elasticity of polyelectrolyte chains into consideration, which makes significant effects as chains are almost fully stretched in the osmotic regime. It is shown that all these factors lead to a non-monotonic behavior for the brush height as a function of the grafting density. At large grafting densities, the brush height increases with increasing the grafting density due to the volume constraint. At small grafting densities, we obtain a re-stretching of the chains for decreasing grafting density, which is caused by lateral electrostatic contributions and is controlled by the counterion-condensation process around polyelectrolyte chains. These results are obtained assuming all counterions to be trapped within the brush, which is valid for sufficiently long chains of large charge fraction.Received: 14 May 2003, Published online: 11 November 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 36.20.-r Macromolecules and polymer molecules - 61.20.Qg Structure of associated liquids: electrolytes, molten salts, etc.     

Microstructure of Polyelectrolyte Nanoaggregates Studied by Fluorescence Probe Method

The microstructure of water soluble nanoaggregates based on polyelectrolyte complex formed by the cationic comb-type copolymer poly(acrylamide -co-[3- (methacryloyl-amino)propyl] trimethylammonium chloride)-graft- polyacrylamide [P(AM-co-MAPTAC)-g-PAM] and the anionic linear polyelectrolyte sodium polyacrylate (NaPA) was investigated using the fluorescence probe technique. The fluorescence probe were 1-anilinonaphthalene-8-sulfonic acid (ANS), pyrene (Py) and 1,10-bis(1-pyrene) decane (PD). The fluorescence properties in polyelectrolyte complex solutions, which are sensitive to either micropolarity (ANS, Py) or microviscosity (PD), were related to the quantities obtained in different pure or mixed solvents. Micropolarities were quantified utilizing the polarity common index (Reichardt) E _T(30). ANS and Py showed a variation of the micropolarity with the charge ratio of the two polymers, with the lowest polarity reached at the complex neutralization. The PD probe, by its excimer-to-monomer fluorescence intensities ratio, enabled us to evidence the effect of the composition and the comb-type copolymer grafting density on the microviscosity of the interpolyelectrolytes aggregates. It has been found that the microviscosity increased with the density of the grafting PAM chains.     

Relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Coulomb-like potential induced by the Lorentz symmetry breaking effects

In this work, we discuss the relativistic Landau–He–McKellar–Wilkens quantization and relativistic bound states solutions for a Dirac neutral particle under the influence of a Coulomb-like potential induced by the Lorentz symmetry breaking effects. We present new possible scenarios of studying Lorentz symmetry breaking effects by fixing the space-like vector field background in special configurations. It is worth mentioning that the criterion for studying the violation of Lorentz symmetry is preserving the gauge symmetry.     

Screening and fundamental length scales in semidilute Na-DNA aqueous solutions

The fundamental length scales in semidilute Na-DNA aqueous solutions have been investigated by dielectric spectroscopy. The low- and the high-frequency relaxation modes are studied in detail. The length scale of the high-frequency relaxation mode at high DNA concentrations can be identified with the de Gennes-Pfeuty-Dobrynin correlation length of polyelectrolytes in semidilute solution, whereas at low DNA concentrations and in the low added salt limit the length scale shows an unusual exponent reminiscent of semidilute polyelectrolyte chains with hydrophobic backbone. The length scale of the low-frequency relaxation mode corresponds to a Gaussian chain composed of correlation blobs in the low added salt limit, and to the Odijk-Skolnick-Fixman value of the single chain persistence length in the high added salt limit.     

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy F_N, depending on N(N - 1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 2⁴ < N < 2⁸ and for an open chain of length 50 < N < 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented. Received 7 June 2001 and Received in final form 17 October 2001     

Thermodynamic and physical properties of FeAl and Fe3Al: an atomistic study by EAM simulation

With this work we present a newly developed potential for the Fe–Al system, which is based on the analytical embedded atom method (EAM) with long range atomic interactions. The potential yields for the two most relevant phases B2-FeAl and D0₃-Fe₃Al lattice constants, elastic constants, as well as bulk and point defect formation enthalpies, which are in good agreement with experimental and other theoretical data. In addition, the phonon dispersions for B2-FeAl and D0₃-Fe₃Al show a good agreement with available experiments. The calculated lattice constants and formation enthalpy for disordered Fe–Al alloys are in good agreement with experimental data or other theoretical calculations. This indicates that the present EAM potentials of Fe–Al system is suitable for atomistic simulations of structural and kinetic properties for the Fe–Al system.     

Second virial coefficient and mechanical moduli of metallic glasses

The relationship between the bulk, shear moduli and second virial coefficient of amorphous materials is derived according to their dependences with the radial distribution function. Lennard-Jones–Gaussian potential is used to investigate the relationship between second virial coefficient and temperature, where Lennard-Jones potential represents interactions with the nearest neighbor atoms, and Gaussian potential is responsible for the multi-atom interactions including the next nearest neighbor atoms and heterogeneous structures for a metallic glass. The results show that deep potential well formed by Gaussian potential causes a large second virial coefficient at low temperatures, which is very obvious for the larger fragility glasses. The quadratic form relationship of shear modulus and compositions is proposed, and confirmed by the experimental results of Pd_xNi_100−x−20P₂₀ alloy.     

Facile synthesis and photocatalytic activity of hierarchical WO3 core–shell microspheres

In this work, we present a facile template-free precipitation method for the large-scale preparation of hierarchical WO₃ core–shell microspheres in which the core was composed of aggregated nanoparticles encapsulated by a hierarchical shell layer self-assembled by ultrafine nanoplates with a thickness of about 15 nm. The products are characterized by X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDS), differential scanning calorimetry and thermogravimetry (TG/DSC). The experimental parameters affecting the morphology were discussed in detail. We found that the concentration of citric acid and pH value of the reaction solution had profound effects on the morphology of the products. In addition, a formation mechanism was proposed for producing hierarchical WO₃ core–shell microspheres. Furthermore, the obtained hierarchical WO₃ core–shell microspheres showed superior photocatalytic activities for the degradation of rhodamine B (RhB) under visible light irradiation.     

Molecular Dynamics simulation of aqueous ZnC12 solutions

An important medium for ore transport within the Earth is by hydrothermal fluids. To understand ore transportation processes by hydrothermal fluids it is necessary to determine the clustering of dissolved ionic species in aqueous solution. We have chosen sphalerite, an important zinc containing mineral, as an example. We describe the results of Molecular Dynamics simulations to predict which chlorozinc complexes will occur at the pressures and temperatures found in the Earth's crust. Potentials have been derived for zinc-water and zinc-chloride interactions using density functional calculations. Although the DFT calculations provide good gas-phase clusters, the resulting potentials do not work well when modelling aqueous solutions. We therefore describe attempts to modify the potential to compensate for these effects. We show that at low chloride concentrations the dominant species are Zn(H₂O)²⁺ ₆, and ZnC1(H₂O)⁺ ₅. At higher temperatures there are a significant number of clusters which contain more than one zinc with bridging chloride ions. In aqueous solutions with a high chloride concentration the dominant species are Zn(H₂O)²⁺ ₆, ZnC1₂(H₂O)⁰ ₄ and ZnC1₃(H₂O)^? ₃. There are almost no clusters containing more than one zinc.     

Dynamic density and spin responses of a superfluid Fermi gas in the BCS–BEC crossover: Path integral formulation and pair fluctuation theory

We present a standard field theoretical derivation of the dynamic density and spin linear response functions of a dilute superfluid Fermi gas in the BCS–BEC crossover in both three and two dimensions. The derivation of the response functions is based on the elegant functional path integral approach which allows us to calculate the density–density and spin–spin correlation functions by introducing the external sources for the density and the spin density. Since the generating functional cannot be evaluated exactly, we consider two gapless approximations which ensure a gapless collective mode (Goldstone mode) in the superfluid state: the BCS–Leggett mean-field theory and the Gaussian-pair-fluctuation (GPF) theory. In the mean-field theory, our results of the response functions agree with the known results from the random phase approximation. We further consider the pair fluctuation effects and establish a theoretical framework for the dynamic responses within the GPF theory. We show that the GPF response theory naturally recovers three kinds of famous diagrammatic contributions: the Self-Energy contribution, the Aslamazov–Lakin contribution, and the Maki–Thompson contribution. We also show that unlike the equilibrium state, in evaluating the response functions, the linear (first-order) terms in the external sources as well as the induced order parameter perturbations should be treated carefully. In the superfluid state, there is an additional order parameter contribution which ensures that in the static and long wavelength limit, the density response function recovers the result of the compressibility (compressibility sum rule). We expect that the f$f$-sum rule is manifested by the full number equation which includes the contribution from the Gaussian pair fluctuations. The dynamic density and spin response functions in the normal phase (above the superfluid critical temperature) are also derived within the Nozières–Schmitt–Rink (NSR) theory.     

Insensitivity to salt of assembly of a rigid biopolymer aggrecan

Many polyelectrolytes, ranging from sulfonated polystyrene to DNA, exhibit a strong sensitivity of their phase behavior to salt concentration, especially to higher valence salts, which often lead to phase separation. We show that the stiff polyelectrolyte aggrecan exhibits a qualitatively different behavior. Specifically, the scattering properties of aggrecan solutions are exceptionally insensitive to the addition of calcium salt, conferring on aggrecan the role of an ion reservoir mediating calcium metabolism in cartilage and bone, and also providing osmotic resilience to compressive load.     

Swelling behavior and viscoelasticity of ultrathin grafted hyaluronic acid films

In this paper we study the effect of monovalent and divalent ions on the swelling behavior and viscoelastic parameters of ultrathin layers of the natural polyelectrolyte hyaluronic acid covalently coupled to glass substrates. A colloidal probe technique is applied for this purpose based on latex beads, hovering over the polymer cushion. By analyzing the vertical Brownian motion of these beads with reflection interference contrast microscopy (RICM) we determined the equilibrium layer thickness (with 3 nm vertical resolution), the interfacial interaction potential, and the characteristic mesh size limiting the hydrodynamic flow within the polyelectrolyte film as a function of the ionic strength. The experimental results are interpreted in terms of three different theoretical models: the polyelectrolyte brush approximation of Pincus [#!ref1!#], a modified polyelectrolyte brush approximation in the high salt concentration limit of Ross and Pincus [#!ref2!#] and the simple scaling approximation for neutral adsorbed polymers of de Gennes [#!ref3!#]. Within experimental error all of these different models fit our experimental data and yield comparable results for the equilibrium layer thickness. Moreover we determine a thickness dependent, effective surface coverage from both brush models. The hydrodynamic properties of the films are interpreted in terms of the Brinkmann model of elastic porous media by assuming an effective mesh size, which depends linearly on the Debye screening length. The salt induced condensation of the polyelectrolyte films can be described microscopically in terms of a progressive contraction of the mesh size with increasing salt concentration. Received 10 September 1998 and Received in final form 30 November 1998     

Effect of counterions on the swelling of spherical polyelectrolyte brushes

We investigate the swelling of colloidal spherical polyelectrolyte brushes in the presence of different counterions. The colloidal particles consist of a solid poly(styrene) core of ca. 100 nm diameter onto which linear polyelectrolyte chains are chemically grafted. Two types of polyelectrolyte chains have been used here: The cationic polyelectrolyte poly(2-(acryloyl)ethyltrimethylammonium chloride)) (PATAC) and the anionic poly(styrenesulfonate) (PSS). Both systems are dispersed in water and the degree of swelling of the surface layer is studied by dynamic light scattering. Adding more and more salt leads to a strong shrinking of the surface layer as expected for polyelectrolyte brushes. It is shown that data obtained at low ionic strength can be collapsed on suitable master curves for monovalent and divalent counterions, respectively. For some ions, however, high salt concentrations may lead to a re-swelling of the brush layer in case of the cationic systems. This points to specific interactions of the counterions with the PATAC chains. This strong specific interaction between the counterions and the attached polyelectrolyte may even lead to flocculation of the particles at intermediate salt concentration. Surprisingly, for iodide and magnesium counterions the solubility increases again if the salt concentration is raised to 1 mol/l. Hence, specific interaction leads to salting-out effects as well as to salting-in effects for these colloidal particles. All specific effects seen at high concentrations of added salt can be explained by the increase of the reduced excluded-volume parameter which is due to the adsorption of salt ions.